The kind of character always gets into trouble by his or her bad luck, silliness, and/or cluelessness. A common source of comedy.
Idiot, dumbass, retard, imbecile, BAKA! All these words describe a person who is not only stupid, but is so incredibly dumb that it becomes a known trait of that person's character. According to TV Tropes, it has become such a staple of anime/manga fandom that some English translators are leaving the word "baka" untranslated.
Often noted in anime when someone shouts some variation of "baka!" as an insult to another person. This word can be used in various forms:
oo-baka "Great Idiot"
origami-tsuki no baka "Acknowledged Idiot" (as in, "you have a degree in dumbassery!")
shoushin shoumei no baka "Just Plain Stupid"
sokonuke no baka "Bottomless Idiot" (as in, "there is no end to your stupidity!")
akireta baka "Hopeless Idiot"
tanjun-baka "Simple Idiot"
usura-baka "Dumb Idiot"
In a few cases, an entire series can revolve around idiots. For example, the manga Hayate x Blade has the word "baka" inserted in the title of every chapter, reflecting both the idiocy of the titular Hayate and the odd behavior of the surrounding cast. Or the anime and manga of Baka to Test, where the dumbest class in school is actually seen in a relatively positive light while still being played for laughs.
There are also cases where a character might be incredibly stupid in one field, yet have good wisdom in another. For example, Hotori Arashiyama is hopeless when it comes to math problems and casual relationships, but her lateral way of thinking leads her to solve mysteries that others have trouble figuring out.